Finite Group DatabasebetaFinite Group Databasebeta| order | 17312 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C541 ⋊ C2 |
| Sylow | C541 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D541 |
| commutator, socle, cosocle | C2×C541 | C24 |
| Fitting | #41×C541 | C2 |
| hypercenter | #41 | D541 |
| hypocenter | C541 | H(5,𝔽2) |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4328 |
Polycyclic presentation:
2^5,541|b^a=be,d^a=de,c^b=ce,f^c=f^540,f^d=f^5402717 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46830341, #46830344, #46830351, … |
| maximal normal subgroup of | #46830341, #46830344, #46830351, … |
| maximal quotient of | #46830647, #46830649, #46830655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17312, 192);